The state could reduce homelessness and save millions in shelter and other costs by finding ways to prevent evictions from public and subsidized housing, according to a report by a nonprofit housing group.

HomeStart Inc., in coordination with the Boston Housing Authority, used its report to track its efforts to intervene in evictions from public housing and to provide financial counseling to poor families. The report said Home Start has prevented more than 500 evictions from the authority’s properties since 2010, not only saving families from homelessness but saving taxpayers thousands of dollars.

Homelessness surged to all-time highs in the state over the past year as rents soared, the state economy slowed, and unemployment remained high. Emergency shelters are overflowing with families, requiring the state to spend millions to place record numbers of people in hotels and motels this winter.

Jessica Rinaldi for The Boston Globe

“I was trapped and I didn’t know how to get out of it,” said Josephine Pizziferri, describing how she was on the brink being evicted before HomeStart helped her pay back rent.

The Boston Housing Authority, the city’s largest landlord and one of the biggest single sources of evictions in the city, began the process of evicting more than 500 people from public housing last year, enough to warrant its own specially designated day each week in Boston housing court.

The vast majority of evicted families must leave due to nonpayment of rent. In some cases, the eviction is forced, requiring a constable and workers who physically remove a family’s belongings from the home. It can be both traumatic for the people involved and expensive for the housing authority.

Each eviction can cost the Boston Housing Authority as much as $10,000, including the expense of hiring a constable and preparing the apartment to be rented again. It costs the state about $2,500 a month to house a family in a homeless shelter. HomeStart paid an average of $800 per household to cover back rent and keep families in their apartments.

HomeStart began its Court Intervention Project in 2010 with nearly $500,000 in grant funding from the Oak Foundation, a Swiss charity that supports social and environmental improvement efforts. The agency targeted evictions involving tenants identified as having the greatest risk of becoming homeless.

Josephine Pizziferri of Jamaica Plain, a mother of three, landed in Boston housing court two years ago because she owed more than $3,000 in rent. She said her boyfriend and father of her children had died in a motorcycle crash in the Dominican Republic and she spent much of her only income from disability checks to fly to the island nation to make funeral arrangements.

She fell far behind on the rent, and the Boston Housing Authority prepared to evict her and her three children, ages 7, 9, and 19, from a townhouse in a privately managed authority development. Then HomeStart intervened, paying $800, helping secure state subsidies to cover another $1,200 of the back rent, and negotiating an installment plan in which Pizziferri paid off $500 and the remaining $500 balance was forgiven.

HomeStart also helped Pizziferri budget her $750 monthly income, designating a third party to automatically pay bills from her bank account each month. She has stayed current since.

“It was a very difficult time for me,” Pizziferri said. “I was trapped and I didn’t know how to get out of it.”

Once an individual or family is evicted from public housing, they are not allowed into the state’s emergency shelter program for two years. HomeStart officials said that families often turn to friends and family, couch surfing for those two years, before ending up in an emergency shelter.

The agency helped 99 households in 2010, 141 in 2011, 144 in 2012, and 166 in 2013, preventing nearly 200 children from becoming homeless each year. Wood-Boyle said none of these families has faced eviction since HomeStart intervened.

The Oak Foundation grant ran out last year. But in a sign of the program’s success, the Boston Housing Authority began paying the $50,000 annual salary of a HomeStart court intervention specialist.

Gail Livingston, director of operations and property management for the authority, said the agency understands the challenges that public housing tenants face but can only do so much. She said the counseling and budgeting assistance from HomeStart helps tenants not repeat their mistakes.

“If there are supports that can help people get their stuff together and get current with their rent,” she said, “that’s a victory as far as we’re concerned.”

Shakenna Appleberry, a 33-year-old mother of two children, 13 and 15, said she was on the brink of eviction last summer for not paying her $130-a-month rent in the West Broadway development in South Boston. She had left a full-time job at a group home helping people with disabilities for a chance to start a radio show, but the project never enlisted enough sponsors to take off.

Unemployed, she fell behind in her rent. At the time of her scheduled eviction, she owed the Boston Housing Authority $297, including late fees.

Appleberry said she considered moving out of state to apply for public housing if evicted, even if it meant uprooting her family. Instead, the HomeStart program paid her debt, helped her budget her income, and, like Pizziferri, designated a third party to ensure that her bills are paid automatically.

The housing court placed her on probation, meaning that if she pays her rent on time for a year, the eviction will be dropped.